文章目录
1.课后习题2.视频课后习题1.课后习题
import numpy as npimport timeimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import Axes3Dfrom pylab import mpl# 图像显示中文mpl.rcParams['font.sans-serif'] = ['Microsoft YaHei']class LogisticRegression:def __init__(self, learn_rate=0.1, max_iter=10000, tol=1e-2):self.learn_rate = learn_rate # 学习率self.max_iter = max_iter # 迭代次数self.tol = tol # 迭代停止阈值self.w = None # 权重def preprocessing(self, X):"""将原始X末尾加上一列，该列数值全部为1"""row = X.shape[0]y = np.ones(row).reshape(row, 1)X_prepro = np.hstack((X, y))return X_preprodef sigmod(self, x):return 1 / (1 + np.exp(-x))def fit(self, X_train, y_train):X = self.preprocessing(X_train)y = y_train.T# 初始化权重wself.w = np.array([[0] * X.shape[1]], dtype=np.float)k = 0for loop in range(self.max_iter):# 计算梯度z = np.dot(X, self.w.T)grad = X * (y - self.sigmod(z))grad = grad.sum(axis=0)# 利用梯度的绝对值作为迭代中止的条件if (np.abs(grad) <= self.tol).all():breakelse:# 更新权重w 梯度上升——求极大值self.w += self.learn_rate * gradk += 1print("迭代次数：{}次".format(k))print("最终梯度：{}".format(grad))print("最终权重：{}".format(self.w[0]))def predict(self, x):p = self.sigmod(np.dot(self.preprocessing(x), self.w.T))print("Y=1的概率被估计为：{:.2%}".format(p[0][0])) # 调用score时，注释掉p[np.where(p > 0.5)] = 1p[np.where(p < 0.5)] = 0return pdef score(self, X, y):y_c = self.predict(X)error_rate = np.sum(np.abs(y_c - y.T)) / y_c.shape[0]return 1 - error_ratedef draw(self, X, y):# 分离正负实例点y = y[0]X_po = X[np.where(y == 1)]X_ne = X[np.where(y == 0)]# 绘制数据集散点图ax = plt.axes(projection='3d')x_1 = X_po[0, :]y_1 = X_po[1, :]z_1 = X_po[2, :]x_2 = X_ne[0, :]y_2 = X_ne[1, :]z_2 = X_ne[2, :]ax.scatter(x_1, y_1, z_1, c="r", label="正实例")ax.scatter(x_2, y_2, z_2, c="b", label="负实例")ax.legend(loc='best')# 绘制p=0.5的区分平面x = np.linspace(-3, 3, 3)y = np.linspace(-3, 3, 3)x_3, y_3 = np.meshgrid(x, y)a, b, c, d = self.w[0]z_3 = -(a * x_3 + b * y_3 + d) / cax.plot_surface(x_3, y_3, z_3, alpha=0.5) # 调节透明度plt.show()# 训练数据集X_train = np.array([[3, 3, 3], [4, 3, 2], [2, 1, 2], [1, 1, 1], [-1, 0, 1], [2, -2, 1]])y_train = np.array([[1, 1, 1, 0, 0, 0]])# 构建实例，进行训练clf = LogisticRegression()clf.fit(X_train, y_train)clf.draw(X_train, y_train)
迭代次数：3232次最终梯度：[ 0.00144779 0.00046133 0.00490279 -0.00999848]最终权重：[ 2.96908597 1.60115396 5.04477438 -13.43744079]
链接3
2.视频课后习题
"""逻辑斯蒂回归算法实现-使用梯度下降"""# 全梯度下降法import numpy as npimport timeimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import Axes3Dimport matplotlib as mpl# mpl.rcParams['font.sans-serif'] = ['SimHei']plt.rcParams['font.sans-serif'] = ['SimHei'] # 用来正常显示中文标签plt.rcParams['axes.unicode_minus'] = False# 用来正常显示负号class LogisticRegression:def __init__(self, learn_rate=0.01, max_iter=10000, tol=1e-2):self.learn_rate = learn_rate # 学习率self.max_iter = max_iter # 迭代次数self.tol = tol # 迭代停止阈值self.w = None # 权重def preprocessing(self, X):"""将原始X末尾加上一列，该列数值全部为1"""row = X.shape[0]y = np.ones(row).reshape(row, 1)X_prepro = np.hstack((X, y))return X_preprodef sigmod(self, x):return 1 / (1 + np.exp(-x))def fit(self, X_train, y_train):X = self.preprocessing(X_train)y = y_train.T# 初始化权重wself.w = np.array([[0] * X.shape[1]], dtype=np.float)k = 0for loop in range(self.max_iter):# 计算梯度z = np.dot(X, self.w.T)grad = X * (y - self.sigmod(z))grad = grad.sum(axis=0)# 利用梯度的绝对值作为迭代中止的条件if (np.abs(grad) <= self.tol).all():breakelse:# 更新权重w 梯度上升——求极大值self.w += self.learn_rate * gradk += 1print("迭代次数：{}次".format(k))print("最终梯度：{}".format(grad))print("最终权重：{}".format(self.w[0]))def predict(self, x):p = self.sigmod(np.dot(self.preprocessing(x), self.w.T))print("Y=1的概率被估计为：{:.2%}".format(p[0][0])) # 调用score时，注释掉p[np.where(p > 0.5)] = 1p[np.where(p < 0.5)] = 0return pdef score(self, X, y):y_c = self.predict(X)error_rate = np.sum(np.abs(y_c - y.T)) / y_c.shape[0]return 1 - error_ratedef draw(self, X, y):# 分离正负实例点y = y[0]X_po = X[np.where(y == 1)]X_ne = X[np.where(y == 0)]# 绘制数据集散点图ax = plt.axes(projection='3d')x_1 = X_po[0, :]y_1 = X_po[1, :]z_1 = X_po[2, :]x_2 = X_ne[0, :]y_2 = X_ne[1, :]z_2 = X_ne[2, :]ax.scatter(x_1, y_1, z_1, c="r", label="正实例")ax.scatter(x_2, y_2, z_2, c="b", label="负实例")ax.legend(loc='best')# 绘制p=0.5的区分平面x = np.linspace(-3, 3, 3)y = np.linspace(-3, 3, 3)x_3, y_3 = np.meshgrid(x, y)a, b, c, d = self.w[0]z_3 = -(a * x_3 + b * y_3 + d) / cax.plot_surface(x_3, y_3, z_3, alpha=0.5) # 调节透明度plt.show()def main():star = time.time()# 训练数据集X_train = np.array([[3, 3, 3], [4, 3, 2], [2, 1, 2], [1, 1, 1], [-1, 0, 1], [2, -2, 1]])y_train = np.array([[1, 1, 1, 0, 0, 0]])# 构建实例，进行训练clf = LogisticRegression()clf.fit(X_train, y_train)# 预测新数据X_new = np.array([[1, 2, -2]])y_predict = clf.predict(X_new)print("{}被分类为：{}".format(X_new[0], y_predict[0]))clf.draw(X_train, y_train)# 利用已有数据对训练模型进行评价X_test=X_trainy_test=y_traincorrect_rate=clf.score(X_test,y_test)print("共测试{}组数据，正确率：{:.2%}".format(X_test.shape[0],correct_rate))end = time.time()print("用时：{:.3f}s".format(end - star))if __name__ == "__main__":main()
迭代次数：10000次最终梯度：[ 0.00483138 0.00138275 0.01561255 -0.03217626]最终权重：[ 2.40550339 1.42893511 3.19459105 -9.63604478]Y=1的概率被估计为：0.00%[ 1 2 -2]被分类为：[0.]Y=1的概率被估计为：100.00%共测试6组数据，正确率：100.00%用时：0.324s
"""逻辑斯蒂回归算法实现-使用随机梯度下降"""# 随机梯度下降法import numpy as npimport timeimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import Axes3Dplt.rcParams['font.sans-serif'] = ['SimHei'] # 用来正常显示中文标签plt.rcParams['axes.unicode_minus'] = False # 用来正常显示负号class LogisticRegression:def __init__(self, learn_rate=0.01, max_iter=10000, tol=1e-3):self.learn_rate = learn_rate # 学习率self.max_iter = max_iter # 迭代次数self.tol = tol # 迭代停止阈值self.w = None # 权重def preprocessing(self, X):"""将原始X末尾加上一列，该列数值全部为1"""row = X.shape[0]y = np.ones(row).reshape(row, 1)X_prepro = np.hstack((X, y))return X_preprodef sigmod(self, x):return 1 / (1 + np.exp(-x))def fit(self, X_train, y_train):X = self.preprocessing(X_train)y = y_train.T# 初始化权重wself.w = np.array([[0] * X.shape[1]], dtype=np.float)i = 0k = 0for loop in range(self.max_iter):# 计算梯度z = np.dot(X[i], self.w.T)grad = X[i] * (y[i] - self.sigmod(z))# 利用梯度的绝对值作为迭代中止的条件if (np.abs(grad) <= self.tol).all():breakelse:# 更新权重w 梯度上升——求极大值self.w += self.learn_rate * gradk += 1# 由于迭代轮数可能超过数据量，所以需要取余i = (i + 1) % X.shape[0]print("迭代次数：{}次".format(k))print("最终梯度：{}".format(grad))print("最终权重：{}".format(self.w[0]))def predict(self, x):p = self.sigmod(np.dot(self.preprocessing(x), self.w.T))print("Y=1的概率被估计为：{:.2%}".format(p[0][0])) # 调用score时，注释掉p[np.where(p > 0.5)] = 1p[np.where(p < 0.5)] = 0print('p=', p)return pdef score(self, X, y):y_c = self.predict(X)error_rate = np.sum(np.abs(y_c - y.T)) / y_c.shape[0]return 1 - error_ratedef draw(self, X, y):# 分离正负实例点y = y[0]X_po = X[np.where(y == 1)]X_ne = X[np.where(y == 0)]# 绘制数据集散点图ax = plt.axes(projection='3d')x_1 = X_po[0, :]y_1 = X_po[1, :]z_1 = X_po[2, :]x_2 = X_ne[0, :]y_2 = X_ne[1, :]z_2 = X_ne[2, :]ax.scatter(x_1, y_1, z_1, c="r", label="正实例")ax.scatter(x_2, y_2, z_2, c="b", label="负实例")ax.legend(loc='best')# 绘制p=0.5的区分平面x = np.linspace(-3, 3, 3)y = np.linspace(-3, 3, 3)x_3, y_3 = np.meshgrid(x, y)a, b, c, d = self.w[0]z_3 = -(a * x_3 + b * y_3 + d) / cax.plot_surface(x_3, y_3, z_3, alpha=0.5) # 调节透明度plt.show()def main():star = time.time()# 训练数据集X_train = np.array([[3, 3, 3], [4, 3, 2], [2, 1, 2], [1, 1, 1], [-1, 0, 1], [2, -2, 1]])y_train = np.array([[1, 1, 1, 0, 0, 0]])# 构建实例，进行训练clf = LogisticRegression()clf.fit(X_train, y_train)# 预测新数据X_new = np.array([[1, 2, -2],[4, 3, 2]])y_predict = clf.predict(X_new)print("{}被分类为：{}".format(X_new[0], y_predict[0]))clf.draw(X_train, y_train)# 利用已有数据对训练模型进行评价# X_test=X_train# y_test=y_train# correct_rate=clf.score(X_test,y_test)# print("共测试{}组数据，正确率：{:.2%}".format(X_test.shape[0],correct_rate))end = time.time()print("用时：{:.3f}s".format(end - star))if __name__ == "__main__":main()
迭代次数：10000次最终梯度：[-0.29285292 -0.29285292 -0.29285292 -0.29285292]最终权重：[ 1.53586681 1.23393345 0.75978189 -4.42286443]Y=1的概率被估计为：12.58%p= [[0.][1.]][ 1 2 -2]被分类为：[0.]用时：0.271s
"""逻辑斯蒂回归算法实现-调用sklearn模块"""from sklearn.linear_model import LogisticRegressionimport numpy as npdef main():# 训练数据集X_train=np.array([[3,3,3],[4,3,2],[2,1,2],[1,1,1],[-1,0,1],[2,-2,1]])y_train=np.array([1,1,1,0,0,0])# 选择不同solver,构建实例，进行训练、测试methodes=["liblinear","newton-cg","lbfgs","sag","saga"]res=[]X_new = np.array([[1, 2, -2]])for method in methodes:clf=LogisticRegression(solver=method,intercept_scaling=2,max_iter=1000)clf.fit(X_train,y_train)# 预测新数据y_predict=clf.predict(X_new)#利用已有数据对训练模型进行评价X_test=X_trainy_test=y_traincorrect_rate=clf.score(X_test,y_test)res.append((y_predict,correct_rate))# 格式化输出methodes=["liblinear","newton-cg","lbfgs ","sag","saga"]# ''.join()-‘delimiter’.join(seq)表示将序列中的元素以指定的字符连接生成一个新的字符串。# seq表示要连接的元素序列、字符串、元组、字典print("solver选择：{}".format(" ".join(method for method in methodes)))print("{}被分类为： {}".format(X_new[0]," ".join(str(re[0]) for re in res)))# round() 方法返回浮点数x的四舍五入值。print("测试{}组数据，正确率： {}".format(X_train.shape[0]," ".join(str(round(re[1],1)) for re in res)))if __name__=="__main__":main()
solver选择：liblinear newton-cg lbfgssag saga[ 1 2 -2]被分类为： [0] [0] [0] [0] [0]测试6组数据，正确率： 1.0 1.0 1.0 1.0 1.0
